ORLANDO, Fla., Dec 2 (Reuters) - Golfer Tiger Woods, engulfed in speculation over his private life after a car accident in the middle of the night, apologized on Wednesday for “transgressions” in a statement that apparently addressed allegations he had extra-marital relationships.

Woods, the world’s No. 1 golfer and a married father of two young children, said in a statement on his website that “I have not been true to my values and the behavior my family deserves.” He did not directly address the allegations of infidelity.

“I have let my family down and I regret those transgressions with all of my heart,” Woods said.[ID:nN02549496]

Companies whose endorsements have helped make Woods perhaps the world’s richest athlete, with a fortune estimated at $1 billion, said they were standing by him.

The golfer suffered facial cuts and bruises when he ran his Cadillac SUV into a fire hydrant and a tree while pulling out of the driveway of his home in Windermere, Florida, about 2 a.m. last Friday.

The time of the accident and Woods’ refusal to meet with police to answer questions about it triggered a storm of speculation. Media outlets have reported that Woods, 33, has had extra-marital relationships with at least three women.

COMPANIES STAND BY GOLFER

One of the world’s most recognizable figures and a powerhouse pitchman with the image of a squeaky clean, hard-working sportsman, Woods has lucrative endorsement deals with major companies such as Nike NIKE.N, AT&T (T.N) and Gillette, a unit of Procter & Gamble (PG.N).

His marketing deals appeared to be holding fast. Nike, Gillette, NetJets and PepsiCo PEP.N’s Gatorade all said their relationships with the golfer remained unchanged.

“Nike supports Tiger and his family. Our relationship remains unchanged,” Beth Gast of Nike Golf said in an e-mail.

The Florida Highway Patrol closed its investigation into the accident on Tuesday and issued a traffic ticket to Woods for careless driving, saying Friday’s accident was his fault but that no criminal charges would be brought.

It said there were no claims of domestic violence made during its investigation. Some media reports had speculated the accident followed a dispute in the Woods household.

An accident report released by the Florida Highway Patrol on Wednesday indicated Woods ran off the road three times as he drove over curbs and onto medians, hitting a hedge in addition to the hydrant and tree. Damages were estimated at $3,300 — $3,000 for the hydrant, $100 for the hedge and $200 for the tree and sod.

Woods issued the statement on his website the morning after US Weekly magazine reported that Jaimee Grubbs, a 24-year-old cocktail waitress from California, claimed to have had a 31-month affair with Woods and said she had saved hundreds of text messages to prove it.

The report was accompanied by a recording of a voicemail message purported to be from Woods to Grubbs in which he warns her to delete her name from her voicemail because his wife had gone through his phone and could be calling her.

‘I AM FAR SHORT OF PERFECT’

“I am not without faults and I am far short of perfect. I am dealing with my behavior and personal failings behind closed doors with my family. Those feelings should be shared by us alone,” Woods said in his statement, adding that “personal sins should not require press releases and problems within a family shouldn’t have to mean public confessions.”

Several days ago, the National Enquirer tabloid said Woods had a relationship with Rachel Uchitel, whom the paper described as a “New York City party girl.” Uchitel has denied any such relationship.

A third publication, Life & Style magazine, reported Woods had been seeing Kalika Moquin, a marketing manager for a Las Vegas nightclub. The magazine said she “neither confirmed nor denied an affair with Tiger.”

In his web posting on Wednesday, Woods also called “utterly false and malicious” reports that physical violence played any role in his car accident. He said his Swedish wife, Elin Nordegren, “has always done more to support our family and shown more grace than anyone could possibly expect.”

Woods paid his $164 traffic fine and is happy with the result of the police probe, his lawyer said.

The top draw on the PGA tour, Woods is chasing Jack Nicklaus’ record for victories in major tournaments and the unofficial title of best golfer ever. He has won 71 times on the tour in a glittering career that includes 14 major wins. (Writing by Jim Loney in Miami, additional reporting by Ben Klayman in New York and Martyn Herman in London; Editing by Pascal Fletcher and Peter Cooney) ((jim.loney@thomsonreuters.com; +1 305 810 2688; Reuters Messaging: jim.loney.reuters.com@reuters.net))